[4] | 1 | SUBROUTINE STRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, |
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| 2 | $ B, LDB ) |
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| 3 | * .. Scalar Arguments .. |
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| 4 | CHARACTER*1 SIDE, UPLO, TRANSA, DIAG |
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| 5 | INTEGER M, N, LDA, LDB |
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| 6 | REAL ALPHA |
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| 7 | * .. Array Arguments .. |
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| 8 | REAL A( LDA, * ), B( LDB, * ) |
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| 9 | * .. |
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| 10 | * |
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| 11 | * Purpose |
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| 12 | * ======= |
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| 13 | * |
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| 14 | * STRSM solves one of the matrix equations |
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| 15 | * |
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| 16 | * op( A )*X = alpha*B, or X*op( A ) = alpha*B, |
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| 17 | * |
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| 18 | * where alpha is a scalar, X and B are m by n matrices, A is a unit, or |
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| 19 | * non-unit, upper or lower triangular matrix and op( A ) is one of |
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| 20 | * |
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| 21 | * op( A ) = A or op( A ) = A'. |
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| 22 | * |
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| 23 | * The matrix X is overwritten on B. |
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| 24 | * |
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| 25 | * Parameters |
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| 26 | * ========== |
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| 27 | * |
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| 28 | * SIDE - CHARACTER*1. |
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| 29 | * On entry, SIDE specifies whether op( A ) appears on the left |
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| 30 | * or right of X as follows: |
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| 31 | * |
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| 32 | * SIDE = 'L' or 'l' op( A )*X = alpha*B. |
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| 33 | * |
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| 34 | * SIDE = 'R' or 'r' X*op( A ) = alpha*B. |
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| 35 | * |
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| 36 | * Unchanged on exit. |
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| 37 | * |
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| 38 | * UPLO - CHARACTER*1. |
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| 39 | * On entry, UPLO specifies whether the matrix A is an upper or |
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| 40 | * lower triangular matrix as follows: |
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| 41 | * |
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| 42 | * UPLO = 'U' or 'u' A is an upper triangular matrix. |
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| 43 | * |
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| 44 | * UPLO = 'L' or 'l' A is a lower triangular matrix. |
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| 45 | * |
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| 46 | * Unchanged on exit. |
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| 47 | * |
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| 48 | * TRANSA - CHARACTER*1. |
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| 49 | * On entry, TRANSA specifies the form of op( A ) to be used in |
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| 50 | * the matrix multiplication as follows: |
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| 51 | * |
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| 52 | * TRANSA = 'N' or 'n' op( A ) = A. |
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| 53 | * |
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| 54 | * TRANSA = 'T' or 't' op( A ) = A'. |
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| 55 | * |
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| 56 | * TRANSA = 'C' or 'c' op( A ) = A'. |
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| 57 | * |
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| 58 | * Unchanged on exit. |
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| 59 | * |
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| 60 | * DIAG - CHARACTER*1. |
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| 61 | * On entry, DIAG specifies whether or not A is unit triangular |
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| 62 | * as follows: |
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| 63 | * |
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| 64 | * DIAG = 'U' or 'u' A is assumed to be unit triangular. |
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| 65 | * |
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| 66 | * DIAG = 'N' or 'n' A is not assumed to be unit |
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| 67 | * triangular. |
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| 68 | * |
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| 69 | * Unchanged on exit. |
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| 70 | * |
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| 71 | * M - INTEGER. |
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| 72 | * On entry, M specifies the number of rows of B. M must be at |
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| 73 | * least zero. |
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| 74 | * Unchanged on exit. |
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| 75 | * |
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| 76 | * N - INTEGER. |
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| 77 | * On entry, N specifies the number of columns of B. N must be |
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| 78 | * at least zero. |
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| 79 | * Unchanged on exit. |
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| 80 | * |
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| 81 | * ALPHA - REAL . |
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| 82 | * On entry, ALPHA specifies the scalar alpha. When alpha is |
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| 83 | * zero then A is not referenced and B need not be set before |
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| 84 | * entry. |
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| 85 | * Unchanged on exit. |
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| 86 | * |
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| 87 | * A - REAL array of DIMENSION ( LDA, k ), where k is m |
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| 88 | * when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. |
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| 89 | * Before entry with UPLO = 'U' or 'u', the leading k by k |
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| 90 | * upper triangular part of the array A must contain the upper |
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| 91 | * triangular matrix and the strictly lower triangular part of |
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| 92 | * A is not referenced. |
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| 93 | * Before entry with UPLO = 'L' or 'l', the leading k by k |
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| 94 | * lower triangular part of the array A must contain the lower |
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| 95 | * triangular matrix and the strictly upper triangular part of |
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| 96 | * A is not referenced. |
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| 97 | * Note that when DIAG = 'U' or 'u', the diagonal elements of |
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| 98 | * A are not referenced either, but are assumed to be unity. |
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| 99 | * Unchanged on exit. |
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| 100 | * |
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| 101 | * LDA - INTEGER. |
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| 102 | * On entry, LDA specifies the first dimension of A as declared |
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| 103 | * in the calling (sub) program. When SIDE = 'L' or 'l' then |
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| 104 | * LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' |
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| 105 | * then LDA must be at least max( 1, n ). |
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| 106 | * Unchanged on exit. |
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| 107 | * |
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| 108 | * B - REAL array of DIMENSION ( LDB, n ). |
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| 109 | * Before entry, the leading m by n part of the array B must |
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| 110 | * contain the right-hand side matrix B, and on exit is |
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| 111 | * overwritten by the solution matrix X. |
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| 112 | * |
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| 113 | * LDB - INTEGER. |
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| 114 | * On entry, LDB specifies the first dimension of B as declared |
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| 115 | * in the calling (sub) program. LDB must be at least |
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| 116 | * max( 1, m ). |
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| 117 | * Unchanged on exit. |
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| 118 | * |
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| 119 | * |
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| 120 | * Level 3 Blas routine. |
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| 121 | * |
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| 122 | * |
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| 123 | * -- Written on 8-February-1989. |
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| 124 | * Jack Dongarra, Argonne National Laboratory. |
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| 125 | * Iain Duff, AERE Harwell. |
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| 126 | * Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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| 127 | * Sven Hammarling, Numerical Algorithms Group Ltd. |
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| 128 | * |
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| 129 | * |
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| 130 | * .. External Functions .. |
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| 131 | LOGICAL LSAME |
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| 132 | EXTERNAL LSAME |
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| 133 | * .. External Subroutines .. |
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| 134 | EXTERNAL XERBLA |
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| 135 | * .. Intrinsic Functions .. |
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| 136 | INTRINSIC MAX |
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| 137 | * .. Local Scalars .. |
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| 138 | LOGICAL LSIDE, NOUNIT, UPPER |
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| 139 | INTEGER I, INFO, J, K, NROWA |
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| 140 | REAL TEMP |
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| 141 | * .. Parameters .. |
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| 142 | REAL ONE , ZERO |
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| 143 | PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) |
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| 144 | * .. |
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| 145 | * .. Executable Statements .. |
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| 146 | * |
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| 147 | * Test the input parameters. |
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| 148 | * |
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| 149 | LSIDE = LSAME( SIDE , 'L' ) |
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| 150 | IF( LSIDE )THEN |
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| 151 | NROWA = M |
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| 152 | ELSE |
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| 153 | NROWA = N |
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| 154 | END IF |
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| 155 | NOUNIT = LSAME( DIAG , 'N' ) |
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| 156 | UPPER = LSAME( UPLO , 'U' ) |
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| 157 | * |
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| 158 | INFO = 0 |
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| 159 | IF( ( .NOT.LSIDE ).AND. |
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| 160 | $ ( .NOT.LSAME( SIDE , 'R' ) ) )THEN |
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| 161 | INFO = 1 |
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| 162 | ELSE IF( ( .NOT.UPPER ).AND. |
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| 163 | $ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN |
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| 164 | INFO = 2 |
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| 165 | ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND. |
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| 166 | $ ( .NOT.LSAME( TRANSA, 'T' ) ).AND. |
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| 167 | $ ( .NOT.LSAME( TRANSA, 'C' ) ) )THEN |
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| 168 | INFO = 3 |
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| 169 | ELSE IF( ( .NOT.LSAME( DIAG , 'U' ) ).AND. |
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| 170 | $ ( .NOT.LSAME( DIAG , 'N' ) ) )THEN |
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| 171 | INFO = 4 |
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| 172 | ELSE IF( M .LT.0 )THEN |
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| 173 | INFO = 5 |
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| 174 | ELSE IF( N .LT.0 )THEN |
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| 175 | INFO = 6 |
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| 176 | ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN |
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| 177 | INFO = 9 |
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| 178 | ELSE IF( LDB.LT.MAX( 1, M ) )THEN |
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| 179 | INFO = 11 |
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| 180 | END IF |
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| 181 | IF( INFO.NE.0 )THEN |
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| 182 | CALL XERBLA( 'STRSM ', INFO ) |
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| 183 | RETURN |
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| 184 | END IF |
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| 185 | * |
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| 186 | * Quick return if possible. |
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| 187 | * |
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| 188 | IF( N.EQ.0 ) |
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| 189 | $ RETURN |
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| 190 | * |
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| 191 | * And when alpha.eq.zero. |
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| 192 | * |
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| 193 | IF( ALPHA.EQ.ZERO )THEN |
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| 194 | DO 20, J = 1, N |
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| 195 | DO 10, I = 1, M |
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| 196 | B( I, J ) = ZERO |
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| 197 | 10 CONTINUE |
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| 198 | 20 CONTINUE |
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| 199 | RETURN |
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| 200 | END IF |
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| 201 | * |
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| 202 | * Start the operations. |
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| 203 | * |
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| 204 | IF( LSIDE )THEN |
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| 205 | IF( LSAME( TRANSA, 'N' ) )THEN |
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| 206 | * |
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| 207 | * Form B := alpha*inv( A )*B. |
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| 208 | * |
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| 209 | IF( UPPER )THEN |
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| 210 | DO 60, J = 1, N |
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| 211 | IF( ALPHA.NE.ONE )THEN |
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| 212 | DO 30, I = 1, M |
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| 213 | B( I, J ) = ALPHA*B( I, J ) |
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| 214 | 30 CONTINUE |
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| 215 | END IF |
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| 216 | DO 50, K = M, 1, -1 |
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| 217 | IF( B( K, J ).NE.ZERO )THEN |
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| 218 | IF( NOUNIT ) |
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| 219 | $ B( K, J ) = B( K, J )/A( K, K ) |
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| 220 | DO 40, I = 1, K - 1 |
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| 221 | B( I, J ) = B( I, J ) - B( K, J )*A( I, K ) |
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| 222 | 40 CONTINUE |
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| 223 | END IF |
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| 224 | 50 CONTINUE |
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| 225 | 60 CONTINUE |
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| 226 | ELSE |
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| 227 | DO 100, J = 1, N |
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| 228 | IF( ALPHA.NE.ONE )THEN |
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| 229 | DO 70, I = 1, M |
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| 230 | B( I, J ) = ALPHA*B( I, J ) |
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| 231 | 70 CONTINUE |
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| 232 | END IF |
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| 233 | DO 90 K = 1, M |
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| 234 | IF( B( K, J ).NE.ZERO )THEN |
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| 235 | IF( NOUNIT ) |
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| 236 | $ B( K, J ) = B( K, J )/A( K, K ) |
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| 237 | DO 80, I = K + 1, M |
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| 238 | B( I, J ) = B( I, J ) - B( K, J )*A( I, K ) |
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| 239 | 80 CONTINUE |
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| 240 | END IF |
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| 241 | 90 CONTINUE |
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| 242 | 100 CONTINUE |
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| 243 | END IF |
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| 244 | ELSE |
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| 245 | * |
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| 246 | * Form B := alpha*inv( A' )*B. |
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| 247 | * |
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| 248 | IF( UPPER )THEN |
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| 249 | DO 130, J = 1, N |
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| 250 | DO 120, I = 1, M |
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| 251 | TEMP = ALPHA*B( I, J ) |
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| 252 | DO 110, K = 1, I - 1 |
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| 253 | TEMP = TEMP - A( K, I )*B( K, J ) |
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| 254 | 110 CONTINUE |
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| 255 | IF( NOUNIT ) |
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| 256 | $ TEMP = TEMP/A( I, I ) |
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| 257 | B( I, J ) = TEMP |
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| 258 | 120 CONTINUE |
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| 259 | 130 CONTINUE |
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| 260 | ELSE |
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| 261 | DO 160, J = 1, N |
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| 262 | DO 150, I = M, 1, -1 |
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| 263 | TEMP = ALPHA*B( I, J ) |
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| 264 | DO 140, K = I + 1, M |
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| 265 | TEMP = TEMP - A( K, I )*B( K, J ) |
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| 266 | 140 CONTINUE |
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| 267 | IF( NOUNIT ) |
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| 268 | $ TEMP = TEMP/A( I, I ) |
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| 269 | B( I, J ) = TEMP |
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| 270 | 150 CONTINUE |
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| 271 | 160 CONTINUE |
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| 272 | END IF |
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| 273 | END IF |
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| 274 | ELSE |
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| 275 | IF( LSAME( TRANSA, 'N' ) )THEN |
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| 276 | * |
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| 277 | * Form B := alpha*B*inv( A ). |
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| 278 | * |
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| 279 | IF( UPPER )THEN |
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| 280 | DO 210, J = 1, N |
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| 281 | IF( ALPHA.NE.ONE )THEN |
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| 282 | DO 170, I = 1, M |
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| 283 | B( I, J ) = ALPHA*B( I, J ) |
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| 284 | 170 CONTINUE |
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| 285 | END IF |
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| 286 | DO 190, K = 1, J - 1 |
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| 287 | IF( A( K, J ).NE.ZERO )THEN |
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| 288 | DO 180, I = 1, M |
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| 289 | B( I, J ) = B( I, J ) - A( K, J )*B( I, K ) |
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| 290 | 180 CONTINUE |
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| 291 | END IF |
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| 292 | 190 CONTINUE |
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| 293 | IF( NOUNIT )THEN |
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| 294 | TEMP = ONE/A( J, J ) |
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| 295 | DO 200, I = 1, M |
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| 296 | B( I, J ) = TEMP*B( I, J ) |
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| 297 | 200 CONTINUE |
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| 298 | END IF |
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| 299 | 210 CONTINUE |
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| 300 | ELSE |
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| 301 | DO 260, J = N, 1, -1 |
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| 302 | IF( ALPHA.NE.ONE )THEN |
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| 303 | DO 220, I = 1, M |
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| 304 | B( I, J ) = ALPHA*B( I, J ) |
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| 305 | 220 CONTINUE |
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| 306 | END IF |
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| 307 | DO 240, K = J + 1, N |
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| 308 | IF( A( K, J ).NE.ZERO )THEN |
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| 309 | DO 230, I = 1, M |
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| 310 | B( I, J ) = B( I, J ) - A( K, J )*B( I, K ) |
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| 311 | 230 CONTINUE |
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| 312 | END IF |
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| 313 | 240 CONTINUE |
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| 314 | IF( NOUNIT )THEN |
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| 315 | TEMP = ONE/A( J, J ) |
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| 316 | DO 250, I = 1, M |
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| 317 | B( I, J ) = TEMP*B( I, J ) |
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| 318 | 250 CONTINUE |
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| 319 | END IF |
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| 320 | 260 CONTINUE |
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| 321 | END IF |
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| 322 | ELSE |
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| 323 | * |
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| 324 | * Form B := alpha*B*inv( A' ). |
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| 325 | * |
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| 326 | IF( UPPER )THEN |
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| 327 | DO 310, K = N, 1, -1 |
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| 328 | IF( NOUNIT )THEN |
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| 329 | TEMP = ONE/A( K, K ) |
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| 330 | DO 270, I = 1, M |
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| 331 | B( I, K ) = TEMP*B( I, K ) |
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| 332 | 270 CONTINUE |
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| 333 | END IF |
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| 334 | DO 290, J = 1, K - 1 |
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| 335 | IF( A( J, K ).NE.ZERO )THEN |
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| 336 | TEMP = A( J, K ) |
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| 337 | DO 280, I = 1, M |
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| 338 | B( I, J ) = B( I, J ) - TEMP*B( I, K ) |
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| 339 | 280 CONTINUE |
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| 340 | END IF |
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| 341 | 290 CONTINUE |
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| 342 | IF( ALPHA.NE.ONE )THEN |
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| 343 | DO 300, I = 1, M |
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| 344 | B( I, K ) = ALPHA*B( I, K ) |
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| 345 | 300 CONTINUE |
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| 346 | END IF |
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| 347 | 310 CONTINUE |
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| 348 | ELSE |
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| 349 | DO 360, K = 1, N |
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| 350 | IF( NOUNIT )THEN |
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| 351 | TEMP = ONE/A( K, K ) |
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| 352 | DO 320, I = 1, M |
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| 353 | B( I, K ) = TEMP*B( I, K ) |
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| 354 | 320 CONTINUE |
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| 355 | END IF |
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| 356 | DO 340, J = K + 1, N |
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| 357 | IF( A( J, K ).NE.ZERO )THEN |
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| 358 | TEMP = A( J, K ) |
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| 359 | DO 330, I = 1, M |
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| 360 | B( I, J ) = B( I, J ) - TEMP*B( I, K ) |
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| 361 | 330 CONTINUE |
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| 362 | END IF |
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| 363 | 340 CONTINUE |
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| 364 | IF( ALPHA.NE.ONE )THEN |
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| 365 | DO 350, I = 1, M |
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| 366 | B( I, K ) = ALPHA*B( I, K ) |
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| 367 | 350 CONTINUE |
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| 368 | END IF |
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| 369 | 360 CONTINUE |
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| 370 | END IF |
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| 371 | END IF |
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| 372 | END IF |
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| 373 | * |
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| 374 | RETURN |
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| 375 | * |
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| 376 | * End of STRSM . |
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| 377 | * |
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| 378 | END |
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